On Coursera, math is written using TeX or LaTeX syntax, enclosed in double-dollar signs , that is,

will look to the reader like

$$a_1b_2 - a_2b_1$$.

For those of you who don't know TeX or LaTeX, I will show you how to write some math expressions that you can use to model your mathematical writing. For a more general overview of the syntax, you may refer to

https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference

Here are a selection of some sample math expressions from this course. Remember to add the double-dollar signs to the math expressions (not added here to prevent MathJax from translating).

(1)

\displaystyle ml\frac{d^2\theta}{dt^2} + cl\frac{d\theta}{dt} + mg\sin{\theta} = F_0\cos{\omega t}

$$\displaystyle ml\frac{d^2\theta}{dt^2} + cl\frac{d\theta}{dt} + mg\sin{\theta} = F_0\cos{\omega t}$$

(2)

\int_1^y \frac{dy}{y^2} = - \int_0^x \sin{x} \,dx

$$\displaystyle \int_1^y \frac{dy}{y^2} = - \int_0^x \sin{x} \,dx$$

(3)

\displaystyle y(x) = \frac{1}{\mu(x)} \left( y_0 + \int_{x_0}^x \mu(x) g(x) \,dx \right)

$$\displaystyle y(x) = \frac{1}{\mu(x)} \left( y_0 + \int_{x_0}^x \mu(x) g(x) \,dx \right)$$

(4)

{\ddot x} + p(t) {\dot x} + q(t) x = 0

$$\ddot x + p(t) \dot x + q(t) x = 0$$

(5)

\displaystyle r_\pm = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}

$$\displaystyle r_\pm = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}$$

(6)

x(t) = e^{\lambda t} \left(A \cos{\mu t} + B \sin{\mu t}\right)

$$x(t) = e^{\lambda t} \left(A \cos{\mu t} + B \sin{\mu t}\right)$$

(7)

y(x) = \sum_{n=0}^\infty a_n x^n

$$\displaystyle y(x) = \sum_{n=0}^\infty a_n x^n$$